A paper was just published that explains this in PLOS One, found here‌​. It looks like it is caused by the formation of a gas cavity in synovial fluid of the joints. They do mention that contrary to what is stated in the previous answer the sound does not come from the collapse of the bubble, but rather its formation. And in response to the comments, as mentioned in the paper, this does not seem to cause any harm to the meniscus or surrounding tissue. See biology.stackexchange.com/a/31582/107
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The NightmanApr 21 at 23:28

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@cagliari2005 - it has overlap but the relief factor is added to it. That justifies it as a new question I think. As more and more questions are asked, more and more questions are closed for being duplicates. As such, subtly different questions should not be closed, but just answered and perhaps linking the other question, or edited first and answered.
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AliceDApr 22 at 1:16

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Nobody really knows where it comes from. The currently most popular theory is that pulling the joint apart leads the gases in the joint's cartilage to accumulate and form a bubble which then pops when you let it spring back. The only thing that has been researched is whether it has an effect on the joint, but people who do it regularly don't seem to have any problems with their joints more than anyone else (I'll find the reference once I have time). Apart from that it's hard to get funding for this kind of research because it has little practical use.

Relief like feeling? That must be subjective to you, I used to do it every now and then but I don't remember getting any relief from it. In that case, it's probably the same relief as other people get from picking their nose, their ears, biting their nails, etc. It's called compensation reaction.

anecdotal I know, but I also enjoy popping my knuckles. May be all in my mind, but I can 'feel' when I haven't for a while, and having done so there is a feeling of 'relief'. People have always told me that it increases your chances of arthritis - if you have a reference that says otherwise I'd much appreciate seeing it also. Thanks
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LukeJun 1 '12 at 8:25